{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,15]],"date-time":"2025-10-15T04:26:33Z","timestamp":1760502393894,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2022,12,18]],"date-time":"2022-12-18T00:00:00Z","timestamp":1671321600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Southwest University of Science and Technology Doctor Fund","award":["20zx7119","62201478","GJCZ-0032-19","2022YFG0148","JCKY2020404C001"],"award-info":[{"award-number":["20zx7119","62201478","GJCZ-0032-19","2022YFG0148","JCKY2020404C001"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["20zx7119","62201478","GJCZ-0032-19","2022YFG0148","JCKY2020404C001"],"award-info":[{"award-number":["20zx7119","62201478","GJCZ-0032-19","2022YFG0148","JCKY2020404C001"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Central Financial Stability Support Special Project","award":["20zx7119","62201478","GJCZ-0032-19","2022YFG0148","JCKY2020404C001"],"award-info":[{"award-number":["20zx7119","62201478","GJCZ-0032-19","2022YFG0148","JCKY2020404C001"]}]},{"name":"Sichuan Science and Technology Program","award":["20zx7119","62201478","GJCZ-0032-19","2022YFG0148","JCKY2020404C001"],"award-info":[{"award-number":["20zx7119","62201478","GJCZ-0032-19","2022YFG0148","JCKY2020404C001"]}]},{"name":"National Defense Basic Research Program","award":["20zx7119","62201478","GJCZ-0032-19","2022YFG0148","JCKY2020404C001"],"award-info":[{"award-number":["20zx7119","62201478","GJCZ-0032-19","2022YFG0148","JCKY2020404C001"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>For system identification under impulsive-noise environments, the gradient-based generalized maximum correntropy criterion (GB-GMCC) algorithm can achieve a desirable filtering performance. However, the gradient method only uses the information of the first-order derivative, and the corresponding stagnation point of the method can be a maximum point, a minimum point or a saddle point, and thus the gradient method may not always be a good selection. Furthermore, GB-GMCC merely uses the current input signal to update the weight vector; facing the highly correlated input signal, the convergence rate of GB-GMCC will be dramatically damaged. To overcome these problems, based on the Newton recursion method and the data-reusing method, this paper proposes a robust adaptive filtering algorithm, which is called the Newton recursion-based data-reusing GMCC (NR-DR-GMCC). On the one hand, based on the Newton recursion method, NR-DR-GMCC can use the information of the second-order derivative to update the weight vector. On the other hand, by using the data-reusing method, our proposal uses the information of the latest M input vectors to improve the convergence performance of GB-GMCC. In addition, to further enhance the filtering performance of NR-DR-GMCC, a random strategy can be used to extract more information from the past M input vectors, and thus we obtain an enhanced NR-DR-GMCC algorithm, which is called the Newton recursion-based random data-reusing GMCC (NR-RDR-GMCC) algorithm. Compared with existing algorithms, simulation results under system identification and acoustic echo cancellation are conducted and validate that NR-RDR-GMCC can provide a better filtering performance in terms of filtering accuracy and convergence rate.<\/jats:p>","DOI":"10.3390\/e24121845","type":"journal-article","created":{"date-parts":[[2022,12,19]],"date-time":"2022-12-19T05:55:43Z","timestamp":1671429343000},"page":"1845","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Newton Recursion Based Random Data-Reusing Generalized Maximum Correntropy Criterion Adaptive Filtering Algorithm"],"prefix":"10.3390","volume":"24","author":[{"given":"Ji","family":"Zhao","sequence":"first","affiliation":[{"name":"School of Information Engineering, Southwest University of Science and Technology, Mianyang 621010, China"}]},{"given":"Yuzong","family":"Mu","sequence":"additional","affiliation":[{"name":"School of Information Engineering, Southwest University of Science and Technology, Mianyang 621010, China"}]},{"given":"Yanping","family":"Qiao","sequence":"additional","affiliation":[{"name":"School of Power and Energy, Northwestern Polytechnical University, Xi\u2019an 710072, China"},{"name":"Science and Technology on Altitude Simulation Laboratory, Mianyang 621700, China"}]},{"given":"Qiang","family":"Li","sequence":"additional","affiliation":[{"name":"School of Information Engineering, Southwest University of Science and Technology, Mianyang 621010, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,12,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Lee, K.A., Gan, W.S., and Kuo, S.M. (2009). Subband Adaptive Filtering: Theory and Implementation, John Wiley & Sons.","DOI":"10.1002\/9780470745977"},{"key":"ref_2","unstructured":"Sayed, A.H. (2011). Adaptive Filters, John Wiley & Sons."},{"key":"ref_3","first-page":"3002","article-title":"Robust constrained generalized correntropy and maximum versoria criterion adaptive filters","volume":"68","author":"Bhattacharjee","year":"2021","journal-title":"IEEE Trans. Circuits Syst. II Express Briefs"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Rusu, A.G., Paleologu, C., Benesty, J., and Ciochin\u0103, S. (2022). A variable step size normalized least-mean-square algorithm based on data reuse. Algorithms, 15.","DOI":"10.3390\/a15040111"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Ozeki, K. (2016). Theory of Affine Projection Algorithms for Adaptive Filtering, Springer.","DOI":"10.1007\/978-4-431-55738-8"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"103452","DOI":"10.1016\/j.dsp.2022.103452","article-title":"M-estimate affine projection spline adaptive filtering algorithm: Analysis and implementation","volume":"123","author":"Yu","year":"2022","journal-title":"Digit. Signal Process."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Sun, X., Ji, J., Ren, B., Xie, C., and Yan, D. (2019). Adaptive forgetting factor recursive least square algorithm for online identification of equivalent circuit model parameters of a lithiumion battery. Energies, 12.","DOI":"10.3390\/en12122242"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"108611","DOI":"10.1016\/j.sigpro.2022.108611","article-title":"Recursive constrained generalized maximum correntropy algorithms for adaptive filtering","volume":"199","author":"Zhao","year":"2022","journal-title":"Signal Process."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"3498","DOI":"10.1109\/TCSI.2020.2993840","article-title":"Projected kernel least mean p-power algorithm: Convergence analyses and modifications","volume":"67","author":"Zhao","year":"2020","journal-title":"IEEE Trans. Circuits Syst. I Regul. Pap."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"108433","DOI":"10.1016\/j.sigpro.2021.108433","article-title":"Robust constrained recursive least M-estimate adaptive filtering algorithm","volume":"194","author":"Xu","year":"2022","journal-title":"Signal Process."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Principe, J.C. (2010). Information Theoretic Learning: Renyi\u2019s Entropy and Kernel Perspectives, Springer Science & Business Media.","DOI":"10.1007\/978-1-4419-1570-2"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"108276","DOI":"10.1016\/j.sigpro.2021.108276","article-title":"Robust and sparsity-aware adaptive filters: A review","volume":"189","author":"Kumar","year":"2021","journal-title":"Signal Process."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"5819","DOI":"10.1109\/TSMC.2019.2957269","article-title":"Minimum error entropy Kalman filter","volume":"51","author":"Chen","year":"2019","journal-title":"IEEE Trans. Syst. Man Cybern. Syst."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Jiang, Z., Li, Y., and Huang, X. (2019). A correntropy-based proportionate affine projection algorithm for estimating sparse channels with impulsive noise. Entropy, 21.","DOI":"10.3390\/e21060555"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Yue, P., Qu, H., Zhao, J., and Wang, M. (2020). Newtonian-type adaptive filtering based on the maximum correntropy criterion. Entropy, 22.","DOI":"10.3390\/e22090922"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Qu, H., Shi, Y., and Zhao, J. (2019). A smoothed algorithm with convergence analysis under generalized maximum correntropy criteria in impulsive interference. Entropy, 21.","DOI":"10.3390\/e21111099"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2379","DOI":"10.1007\/s00034-021-01878-4","article-title":"Polynomial constraint generalized maximum correntropy normalized subband adaptive filter algorithm","volume":"41","author":"Liu","year":"2022","journal-title":"Circuits Syst. Signal Process."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1016\/j.sigpro.2018.06.012","article-title":"Fixed-point generalized maximum correntropy: Convergence analysis and convex combination algorithms","volume":"154","author":"Zhao","year":"2019","journal-title":"Signal Process."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"3376","DOI":"10.1109\/TSP.2016.2539127","article-title":"Generalized correntropy for robust adaptive filtering","volume":"64","author":"Chen","year":"2016","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"107524","DOI":"10.1016\/j.sigpro.2020.107524","article-title":"Generalized maximum correntropy algorithm with affine projection for robust filtering under impulsive-noise environments","volume":"172","author":"Zhao","year":"2020","journal-title":"Signal Process."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Zheng, H., and Qian, G. (2022). Generalized Maximum Complex Correntropy Augmented Adaptive IIR Filtering. Entropy, 24.","DOI":"10.3390\/e24071008"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Yu, Y., He, H., de Lamare, R.C., and Chen, B. (2022). Study of General Robust Subband Adaptive Filtering. arXiv.","DOI":"10.1109\/MLSP55214.2022.9943313"},{"key":"ref_23","unstructured":"Nikias, C.L., and Shao, M. (1995). Signal Processing with Alpha-Stable Distributions and Applications, Wiley-Interscience."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"5286","DOI":"10.1109\/TSP.2007.896065","article-title":"Correntropy: Properties and applications in non-Gaussian signal processing","volume":"55","author":"Liu","year":"2007","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1282","DOI":"10.1109\/TASLP.2020.2982030","article-title":"Robust generalized maximum correntropy criterion algorithms for active noise control","volume":"28","author":"Zhu","year":"2020","journal-title":"IEEE\/ACM Trans. Audio, Speech Lang. Process."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1007\/BF01581275","article-title":"A nonsmooth version of Newton\u2019s method","volume":"58","author":"Qi","year":"1993","journal-title":"Math. Program."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"806","DOI":"10.1080\/00029890.1998.12004968","article-title":"The Newton and Halley methods for complex roots","volume":"105","author":"Yau","year":"1998","journal-title":"Am. Math. Mon."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1016\/j.dsp.2018.09.004","article-title":"A comparative survey of fast affine projection algorithms","volume":"83","author":"Yang","year":"2018","journal-title":"Digit. Signal Process."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1109\/LSP.2010.2040203","article-title":"An affine projection sign algorithm robust against impulsive interferences","volume":"17","author":"Shao","year":"2010","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"11924","DOI":"10.1109\/TVT.2018.2877457","article-title":"Affine projection versoria algorithm for robust adaptive echo cancellation in hands-free voice communications","volume":"67","author":"Huang","year":"2018","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_31","first-page":"86","article-title":"Affine project algorithm based on maximum correntropy criterion for impulsive noise environment","volume":"58","author":"Liu","year":"2018","journal-title":"J. Dalian Univ. Technol."},{"key":"ref_32","unstructured":"Sector, T.S. (2015). Digital network echo cancellers. Series G: Transmission Systems and Meaid, Digital Systems and Netwroks, Recommendation G.168, International Telecommunication Union (ITU-T)."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/12\/1845\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:43:30Z","timestamp":1760147010000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/12\/1845"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,12,18]]},"references-count":32,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2022,12]]}},"alternative-id":["e24121845"],"URL":"https:\/\/doi.org\/10.3390\/e24121845","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2022,12,18]]}}}